Basic Math Examples

$\frac{24 a - 6}{25} \cdot \frac{10}{1 - 4 a}$

Step 1

Simplify terms.

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Step 1.1

Factor $6$ out of $24 a - 6$ .

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Step 1.1.1

Factor $6$ out of $24 a$ .

$\frac{6 (4 a) - 6}{25} \cdot \frac{10}{1 - 4 a}$

Step 1.1.2

Factor $6$ out of $- 6$ .

$\frac{6 (4 a) + 6 (- 1)}{25} \cdot \frac{10}{1 - 4 a}$

Step 1.1.3

Factor $6$ out of $6 (4 a) + 6 (- 1)$ .

$\frac{6 (4 a - 1)}{25} \cdot \frac{10}{1 - 4 a}$

Step 1.2

Cancel the common factor of $5$ .

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Step 1.2.1

Factor $5$ out of $25$ .

$\frac{6 (4 a - 1)}{5 (5)} \cdot \frac{10}{1 - 4 a}$

Step 1.2.2

Factor $5$ out of $10$ .

$\frac{6 (4 a - 1)}{5 \cdot 5} \cdot \frac{5 \cdot 2}{1 - 4 a}$

Step 1.2.3

Cancel the common factor.

$\frac{6 (4 a - 1)}{5 \cdot 5} \cdot \frac{5 \cdot 2}{1 - 4 a}$

Step 1.2.4

Rewrite the expression.

$\frac{6 (4 a - 1)}{5} \cdot \frac{2}{1 - 4 a}$

Step 1.3

Multiply $\frac{6 (4 a - 1)}{5}$ by $\frac{2}{1 - 4 a}$ .

$\frac{6 (4 a - 1) \cdot 2}{5 (1 - 4 a)}$

Step 1.4

Multiply $2$ by $6$ .

$\frac{12 (4 a - 1)}{5 (1 - 4 a)}$

Step 1.5

Cancel the common factor of $4 a - 1$ and $1 - 4 a$ .

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Step 1.5.1

Factor $- 1$ out of $4 a$ .

$\frac{12 (- (- 4 a) - 1)}{5 (1 - 4 a)}$

Step 1.5.2

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{12 (- (- 4 a) - 1 (1))}{5 (1 - 4 a)}$

Step 1.5.3

Factor $- 1$ out of $- (- 4 a) - 1 (1)$ .

$\frac{12 (- (- 4 a + 1))}{5 (1 - 4 a)}$

Step 1.5.4

Rewrite $- (- 4 a + 1)$ as $- 1 (- 4 a + 1)$ .

$\frac{12 (- 1 (- 4 a + 1))}{5 (1 - 4 a)}$

Step 1.5.5

Reorder terms.

$\frac{12 (- 1 (- 4 a + 1))}{5 (- 4 a + 1)}$

Step 1.5.6

Cancel the common factor.

$\frac{12 (- 1 (- 4 a + 1))}{5 (- 4 a + 1)}$

Step 1.5.7

Rewrite the expression.

$\frac{12 \cdot (- 1)}{5}$

Step 2

Multiply $12$ by $- 1$ .

$\frac{- 12}{5}$

Step 3

Move the negative in front of the fraction.

$- \frac{12}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{12}{5}$

Decimal Form:

$- 2.4$

Mixed Number Form:

$- 2 \frac{2}{5}$